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MCQOPTIONS
This section includes 1894 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 1801. |
Consider the system of simultaneous equation,x + 2y + z = 62x + y + 2z = 6x + y + z = 5The system has, |
| A. | infinite number of solutions |
| B. | no solution |
| C. | unique solution |
| D. | exactly two solutions |
| Answer» C. unique solution | |
| 1802. |
A student starts for his school at 9.40 a.m. and comes back home at 4.15 p.m. Determine the time spent by him in the school if half an hour is spent in coming and going. |
| A. | 5 hr 4 min |
| B. | 5 hr |
| C. | 6 hr 5 min |
| D. | 6 hr |
| Answer» D. 6 hr | |
| 1803. |
If x, y are real and \((x - 1)^2 + (y - 4)^2 = 0\), then the value of \(x^3 + y^3\) is |
| A. | 1 |
| B. | 0 |
| C. | 65 |
| D. | 28 |
| Answer» D. 28 | |
| 1804. |
If x4 + x-4 = 194, x > 0, then the value of (x – 2)2 is: |
| A. | 3 |
| B. | 6 |
| C. | 2 |
| D. | 1 |
| Answer» B. 6 | |
| 1805. |
If \(\sqrt x + \frac{1}{{\sqrt x }} = 4\), find the value of \({x^2} + \frac{1}{{{x^2}}}\). |
| A. | 196 |
| B. | 258 |
| C. | 254 |
| D. | 194 |
| Answer» E. | |
| 1806. |
If \(x = \frac{{\sqrt 2 + 1}}{{\sqrt 2 - 1}}\;\)and \(y = \frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}\), then what is the value of x + y? |
| A. | 6 |
| B. | √2 |
| C. | 3 |
| D. | 3√2 |
| Answer» B. √2 | |
| 1807. |
How many integral values of x and y satisfy the equation 5x + 9y = 7, where -500 < x < 500 and -500 < y < 500? |
| A. | 110 |
| B. | 111 |
| C. | 112 |
| D. | None of the above |
| Answer» C. 112 | |
| 1808. |
If \(\vec a, \vec b, \vec c\) are vectors such that \(\vec a + \vec b + \vec c = 0\) and \(|\vec a| = 7, |\vec b| = 5, |\vec c| = 3\), then the angle between the vectors \(\vec b\) and \(\vec c\) is? |
| A. | 60° |
| B. | 30° |
| C. | 45° |
| D. | 90° |
| Answer» B. 30° | |
| 1809. |
If ax = by = cz and b2 = ac, then what is \(\frac{1}{x} + \frac{1}{z}\) equal to? |
| A. | \(\frac{1}{y}\) |
| B. | \(- \frac{1}{y}\) |
| C. | \(\frac{2}{y}\) |
| D. | \(- \frac{2}{y}\) |
| Answer» D. \(- \frac{2}{y}\) | |
| 1810. |
Nature of the roots of the quadratic equation x2 – 4x + 4 = 0 |
| A. | infinite |
| B. | two distinct real roots |
| C. | two equal real roots |
| D. | two complex roots |
| Answer» D. two complex roots | |
| 1811. |
If [(x + 1)/x] = 2, then find the value of \(\left( {\frac{{{x^3}\; + \;1}}{{{x^3}}}} \right) \div \left( {\frac{{{x^{18}}\; + \;1}}{{{x^{18}}}}} \right)\) |
| A. | 2/9 |
| B. | 5 |
| C. | 1 |
| D. | 1/9 |
| Answer» D. 1/9 | |
| 1812. |
Evaluate\(\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{\left( {469 \times 174} \right)}}\) |
| A. | 2 |
| B. | -1 |
| C. | 1 |
| D. | 4 |
| Answer» E. | |
| 1813. |
Let A be a real number. Then the roots of the equation x2 - 4x - log2A = 0 are real and distinct if and only if |
| A. | A < 1/16 |
| B. | A < 1/8 |
| C. | A > 1/16 |
| D. | A > 1/8 |
| Answer» D. A > 1/8 | |
| 1814. |
If a number is as much as greater than 41 as it is less than 83, then what is that number? |
| A. | 68 |
| B. | 49 |
| C. | 62 |
| D. | 51 |
| Answer» D. 51 | |
| 1815. |
Find the quotient: (4x3 - 2x2 - 3) ÷ (2x2 - 1) |
| A. | 2x + 4 |
| B. | 2x - 4 |
| C. | 2x + 1 |
| D. | 2x - 1 |
| Answer» E. | |
| 1816. |
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?A. 10 mB. 14 mC. 12 mD. 8 m |
| A. | B |
| B. | D |
| C. | C |
| D. | A |
| Answer» E. | |
| 1817. |
If (x + iy)(2 - 3i) = 4 - i, find the real values of x and y. |
| A. | x = 14 / 13, y = 5 / 13 |
| B. | x = 5 / 13, y = 14 / 13 |
| C. | x = 2 / 13, y = 1 |
| D. | x = 11/13, y = 10/13 |
| Answer» E. | |
| 1818. |
If (x - 4)3 + (x - 5)3 + (x - 3)3 = 3(x - 4)(x - 5)(x - 3), then what is the value of x? |
| A. | 6 |
| B. | 7 |
| C. | 4 |
| D. | 18 |
| Answer» D. 18 | |
| 1819. |
If a + b + c = 9 and ab + bc + ca = 18, then the value of a3 + b3 + c3 – 3abc is: |
| A. | 243 |
| B. | 254 |
| C. | 234 |
| D. | 244 |
| Answer» B. 254 | |
| 1820. |
If 8(x + y)3 - (x - y)3 = (x + 3y) (Ax2 + Bxy + Cy2), then value of (A - B - C) is: |
| A. | -2 |
| B. | 14 |
| C. | -6 |
| D. | 10 |
| Answer» B. 14 | |
| 1821. |
If x + x – 1 = 2, then the value of x3 + x – 3 is∶ |
| A. | 1 |
| B. | 1/2 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 1822. |
Find the value of x and y if x + y = 6 and 4x + 7y = 36 |
| A. | 2, 4 |
| B. | 4, 2 |
| C. | 1, 1 |
| D. | 0, 0 |
| Answer» B. 4, 2 | |
| 1823. |
If 27(x + y)3 + (x - y)3 = 2(2x + y) (Ax2 + Bxy + Cy2), then what is the value of (A - B + C)? |
| A. | 11 |
| B. | 7 |
| C. | 4 |
| D. | 21 |
| Answer» D. 21 | |
| 1824. |
If a unit vector \(\vec a\;{\rm{makes\;angles\;}}\frac{\pi }{3}\;{\rm{with}}\;\hat i,\frac{\pi }{4}\;{\rm{with}}\;\hat j\) and θ ϵ (0, π) with , then the value of θ is: |
| A. | \(\frac{{5\pi }}{6}\) |
| B. | π/4 |
| C. | \(\frac{{5\pi }}{{12}}\) |
| D. | \(\frac{{2\pi }}{3}\) |
| Answer» E. | |
| 1825. |
If \(x = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }}\), then what is the value of \(\frac{{x + 2\sqrt a }}{{x - 2\sqrt a }} + \frac{{x + 2\sqrt b }}{{x - 2\sqrt b }}\) (when a ≠ b) ? |
| A. | 0 |
| B. | 2 |
| C. | 4 |
| D. | \(\frac{{\sqrt a + \sqrt b }}{{\sqrt a - \sqrt b }}\) |
| Answer» C. 4 | |
| 1826. |
If x2 – 9x – 1 = 0, then what is the value of 5x – 5/x? |
| A. | 35 |
| B. | 45 |
| C. | 24 |
| D. | 33 |
| Answer» C. 24 | |
| 1827. |
If a3 – b3 = 899 and a – b = 29, then (a – b)2 + 3 ab is equal to: |
| A. | 29 |
| B. | 35 |
| C. | 16 |
| D. | 31 |
| Answer» E. | |
| 1828. |
Find the value of :-\(\frac{5.49\times 5.49 \times 5.49 - 1.49 \times 1.49 \times 1.49} {5.49\times 5.49+5.49\times1.49\times+1.49\times1.49}\) |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 1829. |
If a + b + c = 6, a2 + b2 + c2 = 30 and a3 + b3 + c3 = 165, then the value of 4abc is: |
| A. | -1 |
| B. | -4 |
| C. | 1 |
| D. | 4 |
| Answer» E. | |
| 1830. |
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relation among the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among three quantities.A.
|
| A. | A, C |
| B. | E, C |
| C. | A, E |
| D. | A, B |
| E. | B, E |
| Answer» F. | |
| 1831. |
4/5 part of a tank is filled with oil. After taking out 42 litres of oil the tank is 3/4 part full. What is the capacity (in litres) of the tank? |
| A. | 420 |
| B. | 630 |
| C. | 840 |
| D. | 1680 |
| Answer» D. 1680 | |
| 1832. |
If a3 – b3 = 899 and a – b = 31, then (a – b)2 + 3ab is equal to: |
| A. | 29 |
| B. | 35 |
| C. | 16 |
| D. | 31 |
| Answer» B. 35 | |
| 1833. |
If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct? |
| A. | The vectors are parallel |
| B. | The vectors are perpendicular |
| C. | The vectors are anti-parallel |
| D. | The vectors must be unit vectors |
| Answer» C. The vectors are anti-parallel | |
| 1834. |
Let M be a 3 × 3 matrix satisfying:\(M\left[ {\begin{array}{*{20}{c}} 0\\ 1\\ 0 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 1}\\ 2\\ 3 \end{array}} \right],\;M\left[ {\begin{array}{*{20}{c}} 1\\ { - 1}\\ 0 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1\\ 1\\ { - 1} \end{array}} \right],\;and\;M\left[ {\begin{array}{*{20}{c}} 1\\ 1\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\ 0\\ {12} \end{array}} \right]\)Then the sum of the diagonal entries of M is : |
| A. | 9 |
| B. | 12 |
| C. | 6 |
| D. | 0 |
| Answer» B. 12 | |
| 1835. |
If 9 + 2 (3x – xy + x2) + y2 = 0, then what is the value of (3x2 – 2xy + 5y2)? |
| A. | 45 |
| B. | 54 |
| C. | 60 |
| D. | 63 |
| Answer» C. 60 | |
| 1836. |
If 4x + 8 = 7, then x – 3 = ? |
| A. | 1/6 |
| B. | 12/5 |
| C. | -2/4 |
| D. | -13/4 |
| Answer» E. | |
| 1837. |
If \(2a - \frac{2}{a} = 3\), then \(\frac{{4a}}{{{a^2} - a - 1}} = \)? |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | None of the above |
| Answer» E. | |
| 1838. |
If the equation 4x2 - 2kx + 3k = 0 has equal roots, then what are the values of k? |
| A. | 4, 12 |
| B. | 4, 8 |
| C. | 0, 12 |
| D. | 0, 8 |
| Answer» D. 0, 8 | |
| 1839. |
A = (x8 – 1) / (x4 + 1) and B = (y4 – 1) / (y2 + 1). If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2? |
| A. | 96475 |
| B. | 98625 |
| C. | 92425 |
| D. | 89125 |
| Answer» C. 92425 | |
| 1840. |
If x4 + x2y2 + y4 = 37 and x2 – xy + y2 = 5, then what is the value of xy? |
| A. | 1.2 |
| B. | 0 |
| C. | -1 |
| D. | -1.2 |
| Answer» B. 0 | |
| 1841. |
If a matrix is given by A = \(\left[ {\begin{array}{*{20}{c}} 1&2&3\\ 0&4&5\\ 0&0&1 \end{array}} \right]\) , then the determinant of A-1 is: |
| A. | 3 |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{4}\) |
| D. | 4 |
| Answer» D. 4 | |
| 1842. |
Determine the value of \(\frac{{x\; + \;y}}{{x\; + \;2y}}\) when \(\frac{{2x\; + \;y}}{{x\; + \;4y}} = 3\) |
| A. | 3/5 |
| B. | 7/10 |
| C. | 4/5 |
| D. | 10/9 |
| Answer» E. | |
| 1843. |
If x + y + z = 3, and x2 + y2 + z2 = 101, then what is the value of \(\sqrt {{x^3} + {y^3} + {z^3} - 3xyz}\)? |
| A. | 24 |
| B. | 21 |
| C. | 19 |
| D. | 28 |
| Answer» C. 19 | |
| 1844. |
If a + b = 3 and ab = -4, then what is the value of a3 + b3? |
| A. | 36 |
| B. | 63 |
| C. | 12 |
| D. | -15 |
| Answer» C. 12 | |
| 1845. |
If x : y = 2 : 3 then the value of \(\frac{3x + 2y}{9x + 5y}\) will be: |
| A. | \(\frac{4}{11}\) |
| B. | \(\frac{11}{2}\) |
| C. | \(\frac{1}{2}\) |
| D. | \(\frac{5}{14}\) |
| Answer» B. \(\frac{11}{2}\) | |
| 1846. |
If 5x2 - 4x + 7 = 0, then (5x - 2)2 is equal to: |
| A. | -31 |
| B. | 31 |
| C. | 7 |
| D. | 15 |
| Answer» B. 31 | |
| 1847. |
If 8x3 – 27y3 = (Ax + By) (Cx2 – Dy2 + 6xy), then what is the value of (A + B + C – D)? |
| A. | 12 |
| B. | -12 |
| C. | 15 |
| D. | 9 |
| Answer» B. -12 | |
| 1848. |
In how many was can a pair of integers (x, a) be chosen such that x2 - 2 |x| + |a - 2| = 0? |
| A. | 5 |
| B. | 4 |
| C. | 7 |
| D. | 6 |
| Answer» D. 6 | |
| 1849. |
In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. x2 + 7x + 12 = 0II. y2 + 5y + 6 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | Either x = y or Relationship between x and y cannot be established |
| Answer» E. Either x = y or Relationship between x and y cannot be established | |
| 1850. |
A boy travels 2/3rd of the distance of his journey by bus, 1/7th by Rickshaw and 8 km on foot. The total distance travelled by the man is |
| A. | 30 km |
| B. | 36 km |
| C. | 42 km |
| D. | 34 km |
| Answer» D. 34 km | |